In [40]: 
from IPython.display import HTML

HTML('''<script>
code_show=true; 
function code_toggle() {
 if (code_show){
 $('div.input').hide();
 } else {
 $('div.input').show();
 }
 code_show = !code_show
} 
$( document ).ready(code_toggle);
</script>
<form action="javascript:code_toggle()"><input type="submit" value="Click here to toggle on/off the raw code."></form>''')
Out[40]:
In [41]: 
from IPython.display import Image
Image(filename='split/sdgmn3_Page-0.png')
Out[41]:

The Python scripts for all the computations displayed here are available at:

https://github.com/mboudour/GraphMultilayerity

In [42]: 
Image(filename='split/sdgmn3_Page-1.png')
Out[42]:
In [43]: 
Image(filename='split/sdgmn3_Page-2.png')
Out[43]:
In [44]: 
Image(filename='split/sdgmn3_Page-3.png')
Out[44]:
In [45]: 
Image(filename='split/sdgmn3_Page-4.png')
Out[45]:
In [46]: 
Image(filename='split/sdgmn3_Page-5.png')
Out[46]:
In [47]: 
Image(filename='split/sdgmn3_Page-6.png')
Out[47]:

A Sierpinski (Fractal) Self-Similar Graph

In [48]: 
%matplotlib inline
In [49]: 
run SierpinskiCantorGraph.py
In [50]: 
Image(filename='split/sdgmn3_Page-7.png')
Out[50]:
In [51]: 
Image(filename='split/sdgmn3_Page-8.png')
Out[51]:
In [52]: 
Image(filename='split/sdgmn3_Page-9.png')
Out[52]:
In [53]: 
Image(filename='split/sdgmn3_Page-10.png')
Out[53]:
In [54]: 
Image(filename='split/sdgmn3_Page-11.png')
Out[54]:
In [55]: 
Image(filename='split/sdgmn3_Page-12.png')
Out[55]:
In [56]: 
Image(filename='split/sdgmn3_Page-13.png')
Out[56]:


EXAMPLES

1. A Random Bipartite Graph
2. Synthetic 3-Layer Graphs in the Triangular Topology
3. Synthetic 3-Layer Graphs in the 2-Path Topology
4. Analytic 3-Layer Graphs in the Triangular Topology
5. Analytic 3-Layer Graphs in the 2-Path Topology
6. Temporal Graphs with 3 Slices


1. A Random Bipartite Graph

In [57]: 
from bipartite_comm import *
n=7
m=6
p=0.19
G,layer1,layer2,layer3,slayer1,slayer2,edgeList,partition=create_3comms_bipartite(n,m,p)
pos,fig=plot_initial_bgraph(G)
create_colors_per_comm(G,layer1,layer2,layer3,slayer1,slayer2,pos,fig)

n = 7
m = 6
Number of edges = 14
Community1 =  [0, 6, 7]
Community2 =  [1, 3, 5, 8, 9]
Community3 =  [2, 4, 10, 11, 12]
In [58]: 
broken_graph,broken_partition,npartition ,fig= create_node_3attri_graph(G,layer1,layer2,layer3,slayer1,slayer2)
plot_graph_bip_3comms_2set(G,broken_graph,broken_partition,npartition,layer1,layer2,layer3,fig,d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
broken_graph,broken_partition,npartition=create_node_2attri_graph(G,layer1,layer2,layer3,slayer1,slayer2)
plot_graph_bip_2set_3comms(G,broken_graph,broken_partition,npartition,slayer1,slayer2,layer3,fig,d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
In [59]: 
from bipartite_comm import *
n=10
m=10
p=0.23
G,layer1,layer2,layer3,slayer1,slayer2,edgeList,partition=create_3comms_bipartite(n,m,p)
pos,fig=plot_initial_bgraph(G,subp=131)
create_colors_per_comm(G,layer1,layer2,layer3,slayer1,slayer2,pos,fig,subp=132)
create_2colors_per_comm(G,layer1,layer2,layer3,slayer1,slayer2,pos,fig,subp=133)

n = 10
m = 9
Number of edges = 27
Community1 =  [0, 5, 8, 13, 15, 17]
Community2 =  [1, 7, 9, 10, 14]
Community3 =  [2, 3, 4, 6, 11, 12, 16, 18]
In [60]: 
broken_graph,broken_partition,npartition ,fig=create_node_6attri_graph(G,layer1,layer2,layer3,slayer1,slayer2)
plot_graph_bip_3comms_2set(G,broken_graph,broken_partition,npartition,layer1,layer2,layer3,fig,asso=False,d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)

2. Synthetic 3-Layer Graphs in the Triangular Topology

In [61]: 
%matplotlib inline
from syntheticThreeLayerGraph import synthetic_three_level, plot_graph

n1=n2=n3=50
p1=p2=p3=0.01
q1=q2=q3=0.01

G,J,FF,DD,edgeList = synthetic_three_level(n1,n2,n3,p1,p2,p3,q1,q2,q3,no_isolates=False)
pos=plot_graph(G,J,FF,DD,n1,n2,n3,d1=1,d2=10.,d3=0.8,nodesize=50,withlabels=False,edgelist=edgeList,layout=False,b_alpha=0.25)
In [62]: 
from threeLayerCommunityParition import create_node_comm_graph, plot_graph

broken_graph,broken_partition,npartition ,G= create_node_comm_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
In [63]: 
from threeLayerConnComponentsPartition import create_node_conncomp_graph, plot_graph

broken_graph,broken_partition,npartition,G = create_node_conncomp_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
In [64]: 
from threeLayer3AttributesPartition import create_node_3attri_graph, plot_graph

r1=r2=r3=0.333

broken_graph,broken_partition,npartition,G = create_node_3attri_graph(G,J.nodes(),FF.nodes(),DD.nodes(),r1,r2,r3)
plot_graph(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)

3. Synthetic 3-Layer Graphs in the 2-Path Topology

In [65]: 
from syntheticThreeLayerGraph_l import synthetic_three_level, plot_graph

n1=n2=n3=50
p1=p2=p3=0.01
q1=q2=q3=0.01

G,J,FF,DD,edgeList = synthetic_three_level(n1,n2,n3,p1,p2,p3,q1,q2,q3,no_isolates=False)
pos=plot_graph(G,J,FF,DD,n1,n2,n3,d1=2,d2=3.,nodesize=50,withlabels=False,edgelist=edgeList,layout=False,b_alpha=0.25)
In [66]: 
from threeLayerCommunityParition import create_node_comm_graph, plot_graph_stack

broken_graph,broken_partition,npartition,G = create_node_comm_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
In [67]: 
from threeLayerConnComponentsPartition import create_node_conncomp_graph, plot_graph_stack

broken_graph,broken_partition,npartition,G = create_node_conncomp_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
In [68]: 
from threeLayer3AttributesPartition import create_node_3attri_graph, plot_graph_stack

r1=r2=r3=0.333

broken_graph,broken_partition,npartition,G = create_node_3attri_graph(G,J.nodes(),FF.nodes(),DD.nodes(),r1,r2,r3)
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)

4. Analytic 3-Layer Graphs in the Triangular Topology

In [69]: 
from analyticThreeLayerGraph import analyticThreeLayerGraph, plot_graph

n = 150
p = 0.01
r1 = r2 = r3 = 0.333

G, layer1, layer2, layer3, edgeList = analyticThreeLayerGraph(n,p,r1,r2,r3,G_isolates=True)
plot_graph(G,layer1,layer2,layer3,d1=1.5,d2=5.,d3=0.8,nodesize=100,withlabels=False,edgelist=edgeList,layout=False,alpha=0.25)
In [70]: 
from threeLayerCommunityParition import create_node_comm_graph, plot_graph

broken_graph,broken_partition,npartition,G = create_node_comm_graph(G,layer1,layer2,layer3)
plot_graph(G,broken_graph,broken_partition,npartition,layer1,layer2,layer3,d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
In [71]: 
from threeLayerConnComponentsPartition import create_node_conncomp_graph, plot_graph

broken_graph,broken_partition,npartition,G = create_node_conncomp_graph(G,layer1,layer2,layer3)
plot_graph(G,broken_graph,broken_partition,npartition,layer1,layer2,layer3,d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
In [72]: 
from threeLayer3AttributesPartition import create_node_3attri_graph, plot_graph

r1=r2=r3=0.333

broken_graph,broken_partition,npartition,G = create_node_3attri_graph(G,layer1,layer2,layer3,r1,r2,r3)
plot_graph(G,broken_graph,broken_partition,npartition,layer1,layer2,layer3,d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)

5. Analytic 3-Layer Graphs in the 2-Path Topology

In [73]: 
from analyticThreeLayerGraph_l import analyticThreeLayerGraph, plot_graph

n = 150
p = 0.01
r1 = 0.333
r2 = 0.333
r3 = 0.333

G, layer1, layer2, layer3, edgeList = analyticThreeLayerGraph(n,p,r1,r2,r3,G_isolates=True)
plot_graph(G,layer1,layer2,layer3,d1=3.5,d2=5.,d3=0.8,nodesize=100,withlabels=False,edgelist=edgeList,layout=False,alpha=0.2)
In [74]: 
from threeLayerCommunityParition import create_node_comm_graph, plot_graph_stack

broken_graph,broken_partition,npartition,G = create_node_comm_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
In [75]: 
from threeLayerConnComponentsPartition import create_node_conncomp_graph, plot_graph_stack

broken_graph,broken_partition,npartition,G = create_node_conncomp_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)
In [76]: 
from threeLayer3AttributesPartition import create_node_3attri_graph, plot_graph_stack

r1=r2=r3=0.333

broken_graph,broken_partition,npartition,G = create_node_3attri_graph(G,J.nodes(),FF.nodes(),DD.nodes(),r1,r2,r3)
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)

6. Temporal Graph with 3 Slices

In [77]: 
%matplotlib inline
from syntheticThreeLayerGraph_time import synthetic_three_level, plot_graph

p1=p2=p3=0.1
n=50
G,J,FF,DD,JFD,edgeList = synthetic_three_level(n,p1,p2,p3,J_isolates=True,F_isolates=True,D_isolates=True)
#print edgeList
created_pos=plot_graph(n,G,J,FF,DD,JFD,d1=2.,d2=3.,nodesize=50,withlabels=False,edgelist=edgeList,layout=False,b_alpha=0.05) #d=0.5 #d
In [78]: 
from threeLayerCommunityParition import create_node_comm_graph, plot_graph_stack

broken_graph,broken_partition,npartition,G = create_node_comm_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)